| The information contained in options has always been a hot issue in the field of finance research.The difference between the moments under P and Q measures is also one of the concerns.However,the current literature almost explains the risk premium from the demand side.Based on this consideration,this paper attempts to price options from a representative market maker,and then explains the difference between P and Q measures from the supply side perspective.This paper uses mixed normal models for the return to study the impact of downward and upward jump on the risk premium directly and simultaneously.The option price is solved in the framework of minimizing the final wealth variance of the market maker,and the option pricing formula is similar to the addition of multiple Black-Scholes option formulas.By cumulative quantity generating function,moment generating function and model-free method,we have derived analytical solutions for the moments.Three statistical methods are used to estimate parameters,which lays the foundation for parameter settings in subsequent studies.In the application part,firstly this paper shows that the mean,volatility and probability parameters have different effects on the implied volatility smile steepness and skewness;the inability to continuously hedge is not an important reason for the smile shape,while volatility uncertainty can better explain the steepness of the implied volatility smile;the negative skewness under Q measure rather than P measure affects the implied volatility smile tilt,panic which leads to options changes in demand is not necessary for tilt.Secondly volatility risk premium and kurtosis risk premium are mostly negative,while the skewness risk premium is mostly positive.The skewness risk premium and kurtosis risk premium are positively correlated with the statistical mean.In summary,the supply-side option pricing model explains the causes and influencing factors of the risk premium. |
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